I can't possibly provide all the answers here, but I'll cover the basics. Utilize some of these ideas, and I promise your pictures will look better.
1. Charge your batteries. Cold adversely affects the performance of digital camera batteries. Make sure you have a full charge. If it is really cold, keep the batteries inside your coat until you are ready to start shooting.
2. Shoot during the "golden hours". This is the hour after sunrise, and the hour before sunset. The contrast between the warm sunlight and the cool tones in the snow make for dramatic images.
3. This sounds simple, but find an interesting subject. Winter scenes can be very monotone, a splash of color can make all the difference. See covered bridge below:
4. Learn how to use your camera's exposure compensation. The camera can be adjusted, usually in +/- 1/3 stop EV (to geek out on exposure value, read here: http://en.wikipedia.org/wiki/Exposure_value ). The snow is bright, and will fool your camera's light meter. Your pictures will look to dark. Dial in about +1 EV on a cloudy day, and about +2 EV on a sunny day. Shoot an image and chimp the screen, adjust till it looks good. Google "adjust exposure value" for your specific camera for details.
5. Not to sound obvious here, but dress warmly. You are just going to be standing there holding a cold camera. Mittens that open to fingerless gloves allow you to operate camera and keep your digits, waterproof boots save your piggies when you fall in the creek (see covered bridge photo...), and a thermos of coffee is the best way to occupy yourself while you wait for the light.
Winter can be long on the North Coast. Get out and enjoy it with your camera, it'll make scraping your car off on Monday a little less tedious.
Check out some examples below:
PS The EV tip applies to the beach as well. Water and sand reflect light in very much the same way as snow.
PPS That is the Black Dog. Black dog on white snow = tough exposure!